The Emergent Fool » Games

Update on Game-Based High School

plektix — Thu, 29 Jul 2010 15:49:20 +0000

I wrote a while back on a high school that uses games as its primary pedagogical tool. NPR’s All Things Considered has a new report on the school. Excerpt:

“In math, we’re traveling around the world,” says sixth-grader Rocco Rose, a student at Quest to Learn and a citizen of Creepytown — an imaginary city where his class learns math and English. The students play travel agents, convert currencies, keep blogs about their travel experiences and budget trips.

Creepytown is structured like a video game that has jumped out of the computer. During their 10-week “missions,” students learn to adapt and improvise.

“The second trimester, Creepytown went broke,” Salen says. “They had … an economic crisis. So the kids worked to figure out … what had gone wrong. And then they proposed the design of a theme park to bring revenue in.”

Systems Thinking

Salen says playing with complex dynamic systems gives kids opportunities to learn.

Students “learn how to solve problems, how to communicate, how to use data, how to begin to predict things that might be coming down the line,” she says.

They also learn something called systems thinking, which Salen says is one of the cornerstones of 21st century literacy. It helps you understand how the behavior of a derivatives trader in Hong Kong affects housing prices in Florida. When a system becomes sufficiently complex, Salen says, you start to get outcomes that are hard to foresee.

“Suddenly you begin to get what’s called emergent behavior, and in emergent behavior, that system, the elements in it, begin to relate to one another in ways that can be unpredictable,” she says.

Hell yeah! If we can give the next generation early experience with complex systems and unintended consequences, there may be hope for the future yet.

Evolutionary Game Theory and Archaeology

plektix — Tue, 05 Jan 2010 17:01:00 +0000

As a mathematical evolutionary theorist, I use abstract methods to investigate how the structure of an evolutionary process determines whether social behaviors like cooperation can be successful. So I was excited to learn over the holidays (from David Carballo, archaeologist and family friend of my partner) that archaeologists are pursuing the same question from an entirely different angle.

As far as I can understand it, there is a new field of research looking at whether evolutionary game theory (EGT) can help explain major societal shifts. One article looks at the sudden appearance of communal architecture projects in Andes mountain societies (in the second and third millenia B.C.E.) that previously had few permanent buildings. These new constructions appear to be built for use by the entire community, and their construction clearly required large-scale cooperation. Using a combination of EGT and historical arguments, the authors posit that the labor for these projects was not coerced. Rather, the chiefs of these societies were able to mobilize cooperation by enforcing norms of fairness and justice. In their words:

Cooperation does not magically emerge. However, when the appropriate conditions are met, cooperation becomes the adaptive choice of people assessing the costs and benefits of participating in specialized versus nonspecialized labor, loss of autonomy, gain in material wealth and nonmaterial benefits, and degree to which the production and redistribution process is “fair.”

While all cooperative systems are vulnerable to “free-riders”, who attempt to receive benefits without contributing, the authors argue that the combined mechanisms of punishment and group selection (see this post) were sufficient to overcome this difficulty.

I’m excited to see this field taking off in so many different directions, and I’m looking forward to see what new intersections develop!

Highlights from the Year in Ideas

plektix — Mon, 14 Dec 2009 03:07:59 +0000

The New York Times Year in Review section always has some good ones. Some highlights for me from this year:

Does feeling like a fraud make you act like one? Researchers gave experiment subjects designer-style sunglasses from boxes marked “authentic” or “counterfeit”. They then put the subjects in situations with an incentive to be dishonest; far more of the subjects who were told they were wearing counterfeit designer glasses acted in a dishonest manner. Possible conclusion: wearing the “counterfeit” glasses (in reality all the glasses were authentic) made people feel like they were dishonest, and they acted accordingly.
Battle-bots with a moral compass: A roboticist is collaborating with the US army on combat robots (e.g. predator drones) that can weigh military objectives against civilian harm, and adhere to codes of international law. Personally, I’d rather trust human beings with moral decisions, but seeing as we have robots fighting our wars already, putting some safeguards in them is better than nothing.
Proof by blog: Fields medalist mathematician Timothy Gowers decided to run an experiment on his blog by challenging his readers to collaboratively prove a mathematical that he himself could not. Six weeks and hundreds of collaborators later, the theorem was proven, and is planned for publication under the name DHJ Polymath. This success inspired the creation of the polymath project, which aims to advance mathematics through “massively collaborative mathematical research programs”.
Conditional microfinance: The website kickstarter.com matches prospective philanthropists with artists, journalists, inventors, and others needing funding for their projects. The twist: unless a project attracts enough funding to meet its needs, no one pays a dime. So you don’t need to worry about throwing money at something you’re not sure anyone else will invest in; just pledge and see what happens!
SmartTrash Here’s a case where I’m not so excited by the invention itself (a garbage can that scans barcodes items as they go in to see if they can be sold for money) as with the general idea it portends: I’ve always thought of our trash system as one of the worst inefficiencies in our society, in both economical and environmental terms. Outfitting garbage cans with microchips is a possible first step in designing a waste management system that isn’t actually wasteful.

Finally, there’s one “idea” that involves a complete misunderstanding of evolutionary game theory, as far as I can tell. I’ll give this one a separate post when I get around to it.

The Quandaries of Quantifying Complexity

plektix — Thu, 27 Aug 2009 13:09:33 +0000

My good friend and computer scientest Kyle Burke has recently started a highly interesting blog on his research field: combinatorial game theory. The idea of this field is to use games as a tool for studying issues of complexity. Though his blog is only a month old, some important foundational ideas have begun to rear their heads, one of which I’ll explore in this post.

Understanding complexity is important for almost any human endeavor, but defining it in rigorous terms is notoriously difficult. For example, which is the more complicated game, chess or tic-tac-toe? Almost anyone would say chess, but suppose you had a computer that was designed only to play chess. In fact, this computer has no capacity for calculation; it simply has the best move for any given chess position hardwired into its architecture. To get this computer to play tic-tac-toe, you would have to program it to translate each tic-tac-toe position into an analagous chess position, so it could then find the best chess move and translate this move back into tic-tac-toe. This computer would certainly find chess an easier game to play.

Computer scientists have a way around this paradox: instead of looking at individual games or problems, they look at classes of problems. Each problem in the class has a certain size, and they look at how complexity increases in relation to size.

For example, you could easily imagine playing tic-tac-toe on boards of various sizes. Computer scientists can analyze how the complexity of tic-tac-toe varies with the size of the board. (Chess, on the other hand, doesn’t generalize as easily to larger sizes, which makes it difficult to talk about its complexity.)

Unfortunately, if we are faced with a real-world issue (such as how to provide for the needs of a large population), we will want to know the complexity of the specific problem at hand, not how the complexity might theoretically scale with problem size. Part of the reason that complexity issues are so often ignored (to the detriment of many well-meaning policies and programs) is that defining and quantifying complexity is so unavoidably slippery.

A Middle/High School That Teaches Complex Systems Through Games??!

plektix — Thu, 11 Jun 2009 10:20:55 +0000

A new school is opening in New York for grades 6-12 that completely blows my mind. The Quest to Learn school combines games and complex systems in a way that pretty much would have made my life as a teenager. Hell, I wouldn’t mind going back to high school now if I got to go here. I’ll let them describe it:

Mission critical at Quest is a translation of the underlying form of games into a powerful pedagogical model for its 6-12th graders. Games work as rule-based learning systems, creating worlds in which players actively participate, use strategic thinking to make choices, solve complex problems, seek content knowledge, receive constant feedback, and consider the point of view of others. As is the case with many of the games played by young people today, Quest is designed to enable students to “take on” the identities and behaviors of explorers, mathematicians, historians, writers, and evolutionary biologists as they work through a dynamic, challenge-based curriculum with content-rich questing to learn at its core. It’s important to note that Quest is not a school whose curriculum is made up of the play of commercial videogames, but rather a school that uses the underlying design principles of games to create highly immersive, game-like learning experiences. Games and other forms of digital media serve another useful purpose at Quest: they serve to model the complexity and promise of “systems.” Understanding and accounting for this complexity is a fundamental literacy of the 21st century.

Elsewhere they go into a bit more detail about how games are used to teach different subject areas:

At Quest students learn standards‐based content within classes that we call domains. These domains organize disciplinary knowledge in 21st certain ways—around big ideas that require expertise in two or more traditional subjects, like math and science, or ELA and social studies. One of our domains— The Way Things Work—is an integrated math and science class organized around ideas from design and engineering: taking systems apart and putting them back together again. Another domain—Codeworlds—is an integrated ELA, math, and computer programming class organized around the big idea of symbolic systems, language, syntax, and grammar. A third domain—Being, Space and Place—an integrated ELA and social studies class—is organized around the big idea of the individual and their relationship to community and networks of knowledge, across time and space. Wellness is the last of our integrated domains, a class that combines the study of health, socio‐emotional issues, nutrition, movement, organizational strategies, and communication skills.

OMG!OMG!OMG!OMG!

One of my favorite aspects of this school is that they have a separate staff of game designers working together with their teachers. As a former teacher I can tell you that designing good, creative lessons is a relatively different skill-set from actually implementing these lessons in front of a class and following up with your students, and that doing both well requires more time than is physically possible without traveling at relativistic speeds. So having designers who are there at the school and understand the teachers’ needs, and who have the time to make great lessons, is a really really good idea.

Foldit

Rafe Furst — Mon, 25 May 2009 16:25:48 +0000

Has anyone played Foldit, the protein-folding game that is designed to advance the science? This Wired article makes it sound like Ender’s Game meets biochemistry! Sounds like the Poehlman kid is the protein-folding equivalent of Stephen Wiltshire. I love the crowdsourcing, the meta-evolutionary algorithm of it (to find the savants), and the implications for science.

Newcomb's Meta-Paradox

Rafe Furst — Sun, 10 May 2009 19:46:35 +0000

Tweeter, Claus Metzner (@cmetzner) alerted me to this cool area of study with this paper.

Suppose you meet a Wise being (W) who tells you it has put $1,000 in box A, and either $1 million or nothing in box B. This being tells you to either take the contents of box B only, or to take the contents of both A and B. Suppose further that the being had put the $1 million in box B only if a prediction algorithm designed by the being had said that you would take only B. If the algorithm had predicted you would take both boxes, then the being put nothing in box B. Presume that due to determinism, there exists a perfectly accurate prediction algorithm. Assuming W uses that algorithm, what choice should you make?

Ultimately one is lead to understand that the paradox is a manifestation of different interpretations of the problem definition (aren’t all paradoxes though?) If you interpret the setup one way, then you should choose just B and you will net $1M. If another way, then you should choose both and net either $1000 or $1,001,000 depending on W’s unknowable prediction. As the authors conclude:

Newcomb’s paradox takes two incompatible interpretations of a question, with two different answers, and makes it seem as though they are the same interpretation. The lesson of Newcomb’s paradox is just the ancient verity that one must carefully deﬁne all one’s terms.

The authors suggest combining Bayesian nets with game theory is what yields this resolution. And at first I thought they missed the obvious further conclusion from Bayes, which is that you should clearly choose just B. Here was my reasoning. The key clue is in this piece of information: “people seem to divide almost evenly on the problem”. I.e. your Bayesian priors should now be set to 50% on either interpretation. Now, we know that the expected value (EV) of the “just B” scenario is $1M, but we don’t really know what the EV is for the “both boxes” scenario in which “your choice occurs after W has already made its prediction”:

…if W predicted you would take A along with B, then taking both gives you $1,000 rather than nothing. If instead W predicted you would take only B, then taking both boxes yields $1,001,000….

Since in this scenario you are choosing after W’s prediction, is there any way you can “predict” what W’s choice might be? No, of course not, it’s a variant of the Liar’s Paradox where if you predict one thing, the answer is the other. Thus, if we are using a probabilistic approach (as the authors have laid out for us), we must conclude there is no information to be gleaned on W’s prediction and we are forced to assign 50% likelihood of either choice. Hence, the EV of the “both boxes” interpretation is $501,000.

Putting both meta-Bayesian analyses together, we can conclude that since the “just B” interpretation yields $1M and the “both boxes” interpretation yield’s an EV of a little over half that, it’s a no-brainer to choose just B. Which means your EV is exactly $500,000. But wait! We just concluded that the EV for “both boxes” is $501,000, which is clearly better!!!

Newcomb’s paradox will probably crack my list of Top 10 Paradoxes of All-Time (unless I figure out how to solve it after it does).

Game Theory and Military Planning

danielhorowitz — Mon, 04 May 2009 05:12:45 +0000

In “Game Theory: Can a Round of Poker Solve Afghanistan’s Problems?” Major Richard J.H. Gash creates a simple two player game to show how game theory can be used to influence military planning. Gash’s game involves two villages in Afghanistan with the choice to either support the “Coalition” or support the “Taliban.” The scoring of the game generates a payoff matrix that is similar to that of the Prisoner’s Dilemma with a non Pareto-optimal Nash equilibrium. Unfortunately, Gash oversimplifies the game to just one round. In reality, Afghan villages participate in multiple rounds of decision making, with the actual number of rounds unknown, leading to differing strategies and outcomes than those proposed by Gash.

In a single round game with a payoff matrix similar to that proposed by Gash there is a clear Nash equilibrium, representing the optimal strategy both parties will adopt. In this case, both villages choose to support the Taliban. But, supporting the Taliban or Coalition is not a single round game, it is continuous game, with significant but unknown number of rounds. Not only may villages switch allegiance at any time, but if the Taliban is defeated or cleared from the area, the game may abruptly end.

In his seminal work, “The Evolution of Cooperation,” Robert Axelrod explores how cooperation surprisingly trumps competition in a similarly styled prisoner’s dilemma game. Based on an iterated prisoner’s dilemma tournament, Axelrod found that strategies which always defected, (or in the case of Gash’s example, supported the Taliban) performed the worst. The best strategies were mixed, and tended to copy their opponents previous actions, leading to cooperative alliances.

Extending this theory of cooperation to the actions of Afghan villages, we can infer that over time they are likely to discover that cooperation and supporting the coalition is the best strategy. While Gash correctly concludes that changing the cost/benefit value (incentive) for supporting the coalition may speed up the process, it is not necessary to achieve the optimal cooperative solution.

The Challenge

Rafe Furst — Tue, 13 Jan 2009 10:53:58 +0000

Here’s a contest model for spurring innovation that I’d like to explore:

50 participatns ante a pre-determined amount of money
Each participant submits original work (of a pre-determined type)
Each participant votes for one winner (other than themselves)
Winner gets the money

This is similar to other contest models such as biz plan competitions and screenplay competitions, however there are key differences: (1) you put up your own money (2) you judge the winner.

Here are some optional rule variants:

Allow public input (and originality vetting) before voting
Money put up by: participants, organizer, or outside sponsor/investor
Determining winners
- Allow more than one winner
- Use multiple rounds of voting to determine winner
- Bracket tourney (random draw, or use voting round for seeding)
Administrative fee for organizer (who should never be allowed to participate, BTW)
Winner gets non-monetary benefits too
Winner has obligations to fulfill

Depending on the subject matter of the challenge, and the rule variants chosen, you can incentivize a wide range of activity. For example:

Business Plan Competition: Ante $1000; Submissions are one-page exec summaries; Winner gets $50K of seed funding; 5% of equity in the winning startup goes to the other participants as a group.

Social Entrepreneurship: Similar to above except plans are judged on social good as well as profit potential, and participants don’t get equity in the winner.

Charitable Endeavor: Ante is $100, but instead of starting a new organization, the goal is to deploy the funds to existing efforts or individuals or groups in need. Variant: participants volunteer 10 hours of their time in addition to the cash ante.

“TED Prize Wish“: The magic of the TED Prize Wish is that in addition to getting a cash prize, the winner gets to express their wish and have the audience help make it come true. But why should such wishes be eligible to only a select few and judged by a select few?

Creative Endeavors: Here’s your chance to get paid for your brilliant {artwork, photography, original music, musical performance, short story, poetry, youtube video, etc}. Separate challenge for each discipline, $50 ante. Remember, you don’t know what piece your fellow participants will submitted before you ante…

Organizational Improvement: Lots of companies ask their employees (who often know the ins and outs of the business better than top management) to submit ideas on how to improve, with the best ideas being financially rewarded. Here the company provides the prize pool, but the employees themselves vote on the winner(s).

What I like about The Challenge is that it’s flexible and can be organized spontaneously. In fact, I will organize one next week and announce it via this blog, so stay tuned!

Encoding Life's Complexity

Rafe Furst — Wed, 15 Oct 2008 08:29:42 +0000

Will Wright’s demo of Spore illustrates some key concepts of complex systems, including the notion of simple rules generating complex behaviors, and also the power of recursively applied (i.e. fractal) computation at different levels. Living systems leverage these same principles.

One of the baffling aspects of living systems is the relationship of the (relatively small) genome to the seemingly infinite variation and complexity that we witness within and between species. The idea that we share 99% or so of our DNA with mice means that our differences must somehow be accounted for in the remaining 1% (roughly 7 megabytes of information).

The key insight needed to make sense of this mystery involves the aforementioned principles evidenced in the Spore universe, but it also requires the notion of real world as encoding device. By this I mean that the genome itself is not a complete, self-contained piece of code with all that is required to generate (for instance) an adult human. Rather, implicit in the genetic code is a model of the real-world environment that the code will operate in once activated (i.e. “expressed”), and this implicit model is absolutely crucial for life to have originated and continue to thrive. Imagine, for instance, if all of a sudden the laws of chemistry were altered and carbon could only form 2 bonds. Life as we know it would cease to exist; our DNA (and all DNA for that matter) relies implicitly and thoroughly on existing features of the world. And thus our DNA does not need to explicitly encode how to fold proteins since protein-folding is an automatic reaction given the structure and environment of the particular protein molecule.

This implicit encoding or reliance of the genetic code on its environment has been likened to scaffolding that is used in construction (genes being the blueprint of course). But the scaffolding analogy doesn’t do justice to the immensity of information (both in absolute terms and as a percentage of the total) that is implicitly encoded by the environment for use by the genome. Not that this is some giant happy coincidence mind you; the genome evolved in a world where physical and chemical principles pre-existed. And as lifeforms increased in complexity, each new level of organization was a pre-existing condition to be relied upon for the evolution/emergence of the next.

It is worth pointing out that by “genetic environment” I don’t just mean the environment that the whole organism finds itself in, but rather the extended and recursive environment that the genetic code will find itself in as it does its work. This includes increasing levels of complexity that are generated by, or on top of the DNA level: chromosomes, epigenetic markers, proteome, cellular structures, multicellular structures, and on up. One level begets the next, and your genetic code expects these levels to emerge in due course or it won’t function properly (or at all). Consider, for example, how useless the part of your DNA that describes brain structure would be if it were not for the encoding of how to make neurons and axons.

By grasping the significance of the extended, recursive genetic environment (ERGE) it becomes more clear why genetic fatalism is misguided and why the nature/nurture debate misses a large portion of the action. By intervening in the expression of the genome through the ERGE to the mature human animal — for example, via early intervention in childhood — genetic “predispositions” become largely irrelevant in practice. By the same token, there’s no such thing as a purely natural or purely environmental effect: it all a matter of controlling the ERGE.